More coverings by rook domains |
| |
Authors: | A Blokhuis C.W.H Lam |
| |
Affiliation: | Eindhoven University of Technology, Department of Mathematics and Computing Science, Eindhoven, Netherlands;Concordia University, Department of Computer Science, Montreal, Quebec H3G 1M8, Canada |
| |
Abstract: | The set Vkn of all n-tuples (x1, x2,…, xn) with xi?, k is considered. The problem treated in this paper is determining σ(n, k), the minimum size of a set W ? Vkn such that for each x in Vkn, there is an element in W that differs from x in at most one coordinate. By using a new constructive method, it is shown that σ(n, p) ? (p ? t + 1)pn?r, where p is a prime and for some integers t and r. The same method also gives σ(7, 3) ? 216. Another construction gives the inequality σ(n, kt) ? σ(n, k)tn?1 which implies that σ(q + 1, qt) = qq?1tq when q is a prime power. By proving another inequality σ(np + 1, p) ? σ(n, p)pn(p?1), σ(10, 3) ? 5 · 36 and σ(16, 5) ? 13 · 512 are obtained. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|